Question

Rectangle 'R' has area $48$ and integral side-lengths. Which of the following cannot be the ratio of the length of R's longer side to that of its shorter side?

• A. $3:1$
• B. $6:1$
• C. $12:1$
• D. $48:1$

Answer 1

The correct option is B $6:1$

Let longer side be ${}^{\prime }{l}^{\prime }$ and shorter side be ${}^{\prime }{b}^{\prime }$. Then $l\times b=48$

(i) $3:1\Rightarrow 3x\times x=48\Rightarrow x^2=16\Rightarrow x=4$

$l=12,b=4$

(ii) $6:1\Rightarrow 6x\times x=48\Rightarrow x^2=8\Rightarrow x=2\sqrt{2}$

$l=12\sqrt{2},b=2\sqrt{2}$

(iii) $12:1\Rightarrow 12x\times x=48\Rightarrow x^2=4\Rightarrow x=2$

$l=24,b=2$

(iv) $48:1\Rightarrow 48x\times x=48\Rightarrow x^2=1\Rightarrow x=1$

$l=48,b=1$

From (ii) we have seen that the value of $x$ is not a perfect square. Hence $6:1$ is not possible.